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          【LeetCode】1095.山脉数组中查找目标值
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              <time title="创建时间：2020-05-02 19:15:34 / 修改时间：19:14:42" itemprop="dateCreated datePublished" datetime="2020-05-02T19:15:34+08:00">2020-05-02</time>
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        <h4 id="题目描述："><a href="#题目描述：" class="headerlink" title="题目描述："></a>题目描述：</h4><p>给你一个 山脉数组 <code>mountainArr</code>，请你返回能够使得 <code>mountainArr.get(index)</code> 等于 <code>target</code> 最小 的下标 <code>index</code> 值。<a id="more"></a></p>
<p>如果不存在这样的下标 <code>index</code>，就请返回 <code>-1</code>。</p>
<p>何为山脉数组？如果数组<code>A</code> 是一个山脉数组的话，那它满足如下条件：</p>
<p>首先，<code>A.length &gt;= 3</code></p>
<p>其次，在 <code>0 &lt; i &lt; A.length - 1</code> 条件下，存在 <code>i</code> 使得：</p>
<pre>
A[0] < A[1] < ... A[i-1] < A[i]
A[i] > A[i+1] > ... > A[A.length - 1]
</pre>

<p>你将 不能直接访问该山脉数组，必须通过 MountainArray 接口来获取数据：</p>
<p><code>MountainArray.get(k)</code> - 会返回数组中索引为k 的元素（下标从 0 开始）<br><code>MountainArray.length()</code> - 会返回该数组的长度</p>
<p>注意：</p>
<p>对 MountainArray.get 发起超过 100 次调用的提交将被视为错误答案。此外，任何试图规避判题系统的解决方案都将会导致比赛资格被取消。</p>
<p>提示：</p>
<p>   <code>3 &lt;= mountain_arr.length() &lt;= 10000</code></p>
<p>   <code>0 &lt;= target &lt;= 10^9</code></p>
<p>   <code>0 &lt;= mountain_arr.get(index) &lt;= 10^9</code></p>
<h4 id="示例："><a href="#示例：" class="headerlink" title="示例："></a>示例：</h4><pre>
输入：array = [1,2,3,4,5,3,1], target = 3
输出：2
解释：3 在数组中出现了两次，下标分别为 2 和 5，我们返回最小的下标 2。
</pre>


<pre>
输入：array = [0,1,2,4,2,1], target = 3
输出：-1
解释：3 在数组中没有出现，返回 -1。
</pre>

<h4 id="分析："><a href="#分析：" class="headerlink" title="分析："></a>分析：</h4><p>首先可以看到题目要求是不能使用<code>.get()</code>方法超过100次，而且数组最长长度不超过10000，因此想要遍历数组来找是不可行的。再仔细分析一下，其实这个山脉数组是有一定规则排序的，这个数组可以看成由两个有序数组组成的，而这两个有序数组的边界就是山顶元素，于是我们就可以先找出山顶元素，再分别对两个有序数组使用二分查找进行查找。在查找山顶元素时，其实也可以使用二分查找方法，与典型的二分查找情况不同的是，我们每次进行比较是下标<code>mid</code>和<code>mid + 1</code>进行比较。</p>
<p>最坏情况下，我们要使用三次的二分查找，而每次查找的最坏情况下对<code>.get()</code>方法的调用也不超过14次（2^n &lt;= 10000），符合题目不超过100次的限制。</p>
<h4 id="Java实现"><a href="#Java实现" class="headerlink" title="Java实现"></a>Java实现</h4><figure class="highlight excel"><table><tr><td class="gutter"><pre><span class="line">1</span><br><span class="line">2</span><br><span class="line">3</span><br><span class="line">4</span><br><span class="line">5</span><br><span class="line">6</span><br><span class="line">7</span><br><span class="line">8</span><br><span class="line">9</span><br><span class="line">10</span><br><span class="line">11</span><br><span class="line">12</span><br><span class="line">13</span><br><span class="line">14</span><br><span class="line">15</span><br><span class="line">16</span><br><span class="line">17</span><br><span class="line">18</span><br><span class="line">19</span><br><span class="line">20</span><br><span class="line">21</span><br><span class="line">22</span><br><span class="line">23</span><br><span class="line">24</span><br><span class="line">25</span><br><span class="line">26</span><br><span class="line">27</span><br><span class="line">28</span><br><span class="line">29</span><br><span class="line">30</span><br><span class="line">31</span><br><span class="line">32</span><br><span class="line">33</span><br><span class="line">34</span><br><span class="line">35</span><br><span class="line">36</span><br><span class="line">37</span><br><span class="line">38</span><br><span class="line">39</span><br><span class="line">40</span><br><span class="line">41</span><br><span class="line">42</span><br><span class="line">43</span><br><span class="line">44</span><br><span class="line">45</span><br><span class="line">46</span><br><span class="line">47</span><br><span class="line">48</span><br><span class="line">49</span><br><span class="line">50</span><br><span class="line">51</span><br><span class="line">52</span><br><span class="line">53</span><br><span class="line">54</span><br><span class="line">55</span><br><span class="line">56</span><br><span class="line">57</span><br><span class="line">58</span><br><span class="line">59</span><br><span class="line">60</span><br><span class="line">61</span><br><span class="line">62</span><br><span class="line">63</span><br><span class="line">64</span><br><span class="line">65</span><br><span class="line">66</span><br><span class="line">67</span><br><span class="line">68</span><br><span class="line">69</span><br><span class="line">70</span><br><span class="line">71</span><br><span class="line">72</span><br><span class="line">73</span><br><span class="line">74</span><br></pre></td><td class="code"><pre><span class="line">/**</span><br><span class="line"> * // This is MountainArray's API interface.</span><br><span class="line"> * // You should <span class="built_in">not</span> implement it, <span class="built_in">or</span> speculate about its implementation</span><br><span class="line"> * interface MountainArray &#123;</span><br><span class="line"> *     public <span class="built_in">int</span> get(<span class="built_in">int</span> <span class="built_in">index</span>) &#123;&#125;</span><br><span class="line"> *     public <span class="built_in">int</span> length() &#123;&#125;</span><br><span class="line"> * &#125;</span><br><span class="line"> */</span><br><span class="line"> </span><br><span class="line">class Solution &#123;</span><br><span class="line">    public <span class="built_in">int</span> findInMountainArray(<span class="built_in">int</span> target, MountainArray mountainArr) &#123;</span><br><span class="line">        <span class="built_in">int</span> <span class="built_in">max</span> = findMaxIndex(mountainArr);    //山顶元素坐标</span><br><span class="line">        <span class="built_in">int</span> <span class="built_in">len</span> = mountainArr.length();</span><br><span class="line">        <span class="built_in">if</span>(target == mountainArr.get(<span class="built_in">max</span>))&#123;</span><br><span class="line">            return <span class="built_in">max</span>;</span><br><span class="line">        &#125;</span><br><span class="line">        return searchLeft(<span class="number">0</span>,<span class="built_in">max</span>-<span class="number">1</span>,mountainArr,target) == -<span class="number">1</span>?</span><br><span class="line">                searchRight(<span class="built_in">max</span>+<span class="number">1</span>,<span class="built_in">len</span> - <span class="number">1</span>,mountainArr,target)<span class="symbol">:</span></span><br><span class="line">                searchLeft(<span class="number">0</span>,<span class="built_in">max</span>-<span class="number">1</span>,mountainArr,target);</span><br><span class="line">                </span><br><span class="line">    &#125;</span><br><span class="line">    /**找出山顶元素</span><br><span class="line">     * @Param [mountainArray]</span><br><span class="line">     * @return <span class="built_in">int</span></span><br><span class="line">     */</span><br><span class="line">    public <span class="built_in">int</span> findMaxIndex(MountainArray mountainArray) &#123;</span><br><span class="line">        <span class="built_in">int</span> <span class="built_in">left</span> = <span class="number">0</span>;</span><br><span class="line">        <span class="built_in">int</span> <span class="built_in">right</span> = mountainArray.length() - <span class="number">1</span>;</span><br><span class="line">        <span class="built_in">int</span> <span class="built_in">mid</span> = <span class="built_in">left</span>;</span><br><span class="line">        while (<span class="built_in">left</span> &lt; <span class="built_in">right</span>) &#123;</span><br><span class="line">            <span class="built_in">mid</span> = <span class="built_in">left</span> + (<span class="built_in">right</span> - <span class="built_in">left</span>) / <span class="number">2</span>;</span><br><span class="line">            <span class="built_in">if</span> (mountainArray.get(<span class="built_in">mid</span>) &lt; mountainArray.get(<span class="built_in">mid</span> + <span class="number">1</span>)) &#123;</span><br><span class="line">                <span class="built_in">left</span> = <span class="built_in">mid</span> + <span class="number">1</span>;</span><br><span class="line">            &#125; else &#123;</span><br><span class="line">                <span class="built_in">right</span> = <span class="built_in">mid</span>;</span><br><span class="line">            &#125;</span><br><span class="line">        &#125;</span><br><span class="line">        return <span class="built_in">left</span>;</span><br><span class="line">    &#125;</span><br><span class="line">    </span><br><span class="line">    public <span class="built_in">int</span> searchLeft(<span class="built_in">int</span> start, <span class="built_in">int</span> end, MountainArray mountainArray, <span class="built_in">int</span> target) &#123;</span><br><span class="line">        <span class="built_in">int</span> <span class="built_in">left</span> = start;</span><br><span class="line">        <span class="built_in">int</span> <span class="built_in">right</span> = end;</span><br><span class="line">        <span class="built_in">int</span> <span class="built_in">mid</span> = start;</span><br><span class="line">        while (<span class="built_in">left</span> &lt;= <span class="built_in">right</span>) &#123;</span><br><span class="line">            <span class="built_in">mid</span> = <span class="built_in">left</span> + (<span class="built_in">right</span> - <span class="built_in">left</span>) / <span class="number">2</span>;</span><br><span class="line">            <span class="built_in">if</span> (mountainArray.get(<span class="built_in">mid</span>) == target) &#123;</span><br><span class="line">                return <span class="built_in">mid</span>;</span><br><span class="line">            &#125;else <span class="built_in">if</span> (mountainArray.get(<span class="built_in">mid</span>) &lt; target) &#123;</span><br><span class="line">                <span class="built_in">left</span> = <span class="built_in">mid</span> + <span class="number">1</span>;</span><br><span class="line">            &#125; else &#123;</span><br><span class="line">                <span class="built_in">right</span> = <span class="built_in">mid</span> - <span class="number">1</span>;</span><br><span class="line">            &#125; </span><br><span class="line">        &#125;</span><br><span class="line">        return -<span class="number">1</span>;  //没找到</span><br><span class="line">    &#125;</span><br><span class="line"></span><br><span class="line">    public <span class="built_in">int</span> searchRight(<span class="built_in">int</span> start, <span class="built_in">int</span> end, MountainArray mountainArray, <span class="built_in">int</span> target) &#123;</span><br><span class="line">        <span class="built_in">int</span> <span class="built_in">left</span> = start;</span><br><span class="line">        <span class="built_in">int</span> <span class="built_in">right</span> = end;</span><br><span class="line">        <span class="built_in">int</span> <span class="built_in">mid</span> = <span class="built_in">left</span>;</span><br><span class="line">        while (<span class="built_in">left</span> &lt;= <span class="built_in">right</span>) &#123;</span><br><span class="line">            <span class="built_in">mid</span> = <span class="built_in">left</span> + (<span class="built_in">right</span> - <span class="built_in">left</span>) / <span class="number">2</span>;</span><br><span class="line">            <span class="built_in">if</span> (mountainArray.get(<span class="built_in">mid</span>) == target) &#123;</span><br><span class="line">                return <span class="built_in">mid</span>;</span><br><span class="line">            &#125;else <span class="built_in">if</span> (mountainArray.get(<span class="built_in">mid</span>) &lt; target) &#123;</span><br><span class="line">                <span class="built_in">right</span> = <span class="built_in">mid</span> - <span class="number">1</span>;</span><br><span class="line">            &#125; else &#123;</span><br><span class="line">                <span class="built_in">left</span> = <span class="built_in">mid</span> + <span class="number">1</span>;</span><br><span class="line">            &#125; </span><br><span class="line">        &#125;</span><br><span class="line">        return -<span class="number">1</span>;  //没找到</span><br><span class="line">    &#125;</span><br><span class="line">&#125;</span><br></pre></td></tr></table></figure>
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